> But corner point #2 doesn't.

That's because the 2 segments that are touching at that point have matching tangents. So even though it's a "corner" point which will make a kink if you move it around, it is completely smooth at that spot in its current point arrangement.

Since each segment has the same tangent direction at that spot, the edges of the resulting surface match up there as well.

The other one that was a problem seemed to look smooth to the eye, but it was off by just enough (0.68 degrees) to make a non-tangent area in the curve right there.

- Michael